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1

Managing Smile risk from Hagan et. al. Generally if you pre-select $\beta$, it is from a priori considerations. $\beta = 1$ corresponds to stochastic lognormal $\beta = 0$ is stochastic normal $\beta=1/2$ CIR In the SABR model, beta is usually calibrated first, followed by the other 3 parameters. Frequently, instead of calibrating beta, it is simply ...


2

This is an interesting question. Peter A is correct that SV is typically combined with LV these days to get the so called SLV (stochastic local vol model). There is no obvious definition for Greeks here as there are no closed form solutions. Depending on the implementation, it will likely be based on a finite-difference solver of the PDE or Monte Carlo (MC) ...


2

Starting with $$dS_t = rS_tdt +\sigma_t S_tdW_t,$$ Ito Lemma in two steps gives: $$d\log S_t = S_t^{-1} dS_t - 2^{-1}S_t^{-2} (dS_t)^2 \; \; \; (*)$$ $$d\log S_t = (r-2^{-1}\sigma^2_t) dt + \sigma_t dW_t \; \; \; (**)$$ From (**) (and starting SDE) we get $$ d[\log S]_t = (d\log S_t)^2 = \sigma_t^2 dt = S_t^{-2} (dS_t)^2 $$ From (*) we then get: $$ d\log ...


0

Risk.net: Calling out autocallable pricing offers an intuitive explanation of modelling issues with autocallables with baskets. Since the vast majority of AC are based on baskets, this is very relevant. LV is simply insufficient. I like this tweet, it's funny and accurate at the same time. The same guy has a rant that explains issues with AC pricing quite ...


3

A similar question posted after this one has a very good answer. Especially the section that explains that the calibrated leverage surface is typically observed to flatten with maturity (a shortcoming of LV). Therefore the forward volatility smile will be less convex than on the initial pricing date and you will not be pricing deals properly which are ...


4

Maybe this deck by Jim Gatheral would help get the intuition, see slides 10 and following. The dynamics you mentioned is obtained by: Looking at the Bergomi dynamics for the forward variance process; Assuming there is only one factor driving the dynamics; Noticing a similarity with a rough process when replacing the Bergomi exponential kernel by a Riemann-...


4

The numerical approximation of the call option price in the Heston model is notoriously unstable and can easily lead to imprecise answers for extreme parameter. Several different formulas exist for computing the price with some being more stable than others. The formula you are using is arguably one of the worst ones. The most precise algorithm I know of is ...


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